Question: Solve for $e$. Give an exact answer. $0.75(8+e)=2-1.25e$ $e =$
Solution: We need to manipulate the equation to get $ e $ by itself. $\begin{aligned} 0.75(8+e) &= 2-1.25e \\\\ 6+0.75e &= 2-1.25e~~~~~~~~~~\gray{\text{Distribute}}\\\\ 6+0.75e{+1.25e} &= 2-1.25e{+1.25e} ~~~~~~~~~~\gray{\text{Add 1.25e to each side}}\\\\ 6+2e&=2 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 6+2e{-6} &= 2{-6} ~~~~~~~~~~\gray{\text{Subtract 6 from each side}}\\\\ 2e &= -4~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{2e}{{2}}&= \dfrac{-4}{{2}}~~~~~~~~~~\gray{\text{Divide each side by 2}} \\\\ e &= {-2} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ e= { -2 }~~~~~~~~$ [Let's check our work!]